Gaussian almost primes in almost all narrow sectors

Gaussian almost primes in almost all narrow sectors

We show that almost all sectors of the disc \{z \in \mathbb{C}: |z|^2\leq X\} of area (\log X)^{15.1} contain products of exactly two Gaussian primes, and that almost all sectors of area (\log X)^{1 + \varepsilon} contain products of exactly three Gaussian primes. The argument is based on mean value...

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Veröffentlicht in:Revista matemática iberoamericana 2024-08, Vol.40 (4), p.1293-1350
Hauptverfasser: Jarviniemi, Olli, Teravainen, Joni
Format: Artikel
Sprache:eng
Schlagworte:
Gaussian processes
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Zusammenfassung:We show that almost all sectors of the disc \{z \in \mathbb{C}: |z|^2\leq X\} of area (\log X)^{15.1} contain products of exactly two Gaussian primes, and that almost all sectors of area (\log X)^{1 + \varepsilon} contain products of exactly three Gaussian primes. The argument is based on mean value theorems, large value estimates and pointwise bounds for Hecke character sums.
ISSN:0213-2230
2235-0616
DOI:10.4171/RMI/1452